Nav’s loan calculators have become quite popular. I didn’t put a lot of thoughts on it when I published the first few calculators. I am a software engineer/statistician by training. <brag>Writing the calculators came natural to me as I had worked on tools that are 100 times more sophisticated to predict ad clicks when I was at Facebook </brag>. It was just something convenient for Nav to communicate and compare the costs across different financing products. Now, as the calculators become more widely used and probably 50+ people asked me how the math works, it’s time to explain the math in detail and clarify the assumptions and terms we use. We will be publishing one post per calculator and we will start with the Merchant Cash Advance APR calculator.

The APR for a merchant cash advance is actually not deterministic as the payment is based on the percentage of revenue. For example, if you are supposed to pay 8% of your card sales and the averaged card sales for the past few months have been $20,000, you can estimate your APR based on the $20,000 * 8% = $1,600 payment. But if your actual card sales are $30,000 or $15,000 in first month after you get the advance, you will actually be paying $2,400 and $1,200 for the first month. This will either increase or decrease your APR. Our MCA calculator is assuming that your monthly card sales will be constant until you pay off the advance and it’s the amount you specify in the Projected Monthly Card Sales field.

Another assumption we made is that we do daily compounding. What this means is that we assume and calculate the APR as follows:

1. There are 30 days in a month
2. Each day, the revenue is constant and is equal to (Projected Monthly Sales)/30
3. The Daily Payment is equal_to *(Projected Monthly Sales)/30 (% of Future Card Sales)**
4. Number of Payments is equal_to (Payback Amount)/(Daily Payment)
5. Daily Rate is equal to the result of the excel formula of =RATE(Number of Payments, Daily Payment, -(Advanced Amount))
6. APR is equal to *(Daily Rate) 365**. We assume there’s 365 days in a year.

Different choices on number of days in a month or number of days in a year will result in slightly different results. For high APR advances, the difference between daily and monthly compounding will have a non-negligible difference. But we stick with daily compounding because merchant’s account is debited daily. The APR calculator is meant to be used as a benchmark tool to compare across different products. For most of the time, the difference in APR is large enough to tell if product A is more expensive than product B. We also advise people to compare not only the APR but the overall costs given similar repayment periods.

If you are really into math, you can also calculate the APR after the fact based on what you actually paid using Excel as follows.

1. Put -(Advanced Amount) into cell A1
2. Put the series of daily payments into cell A2, A3 … A_n
3. Figure out the Daily Rate is equal to =IRR(A1:A_n)
4. APR is equal to *(Daily Rate)365**

If your card sales are relatively constant, you should see an APR similar to our MCA calculator if you put your actual averaged monthly sales into the Projected Monthly Sales field.

We will be talking about the math of our business term loan apr calculator in the next post and we will have an example using both calculators to compare a merchant cash advance to a credit card advance. Stay tuned!